Invertible bimodule categories over the representation category of a Hopf algebra

Bojana Femic; Adriana Mejia Castaño; Martin Mombelli

Invertible bimodule categories over the representation category of a Hopf algebra

Quantum Algebra 2014-02-13 v1

Authors: Bojana Femic , Adriana Mejia Castaño , Martin Mombelli

Abstract

For any finite-dimensional Hopf algebra $H$ we construct a group homomorphism $\biga(H)\to \text{BrPic}(\Rep(H))$ , from the group of equivalence classes of $H$ -biGalois objects to the group of equivalence classes of invertible exact $\Rep(H)$ -bimodule categories. We discuss the injectivity of this map. We exemplify in the case $H=T_q$ is a Taft Hopf algebra and for this we classify all exact indecomposable $\Rep(T_q)$ -bimodule categories.

Keywords

hopf algebra representation category invertible bimodule categories bi-galois objects brauer-picard group taft algebra

Cite

@article{arxiv.1402.2955,
  title  = {Invertible bimodule categories over the representation category of a Hopf algebra},
  author = {Bojana Femic and Adriana Mejia Castaño and Martin Mombelli},
  journal= {arXiv preprint arXiv:1402.2955},
  year   = {2014}
}

Comments

26 pages. Accepted in Journal of Pure and Applied Algebra

Invertible bimodule categories over the representation category of a Hopf algebra

Abstract

Keywords

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